Wavelength division multiplexed (WDM) optical communication systems (referred to as “WDM systems”) are systems in which multiple optical signals, each having a different wavelength, are combined onto a single optical fiber using an optical multiplexer circuit (referred to as a “multiplexer”). Such systems may include an optical transmitter (Tx), such as a laser associated with each wavelength, a modulator configured to modulate the output of the laser, and a multiplexer to combine each of the modulated outputs (e.g., to form a combined output or WDM signal). Dual-polarization (DP) (also known as polarization multiplex (PM)) is sometimes used in coherent optical modems. An optical transmitter may be associated with a polarization beam combiner (PBC) that combines two optical signals into a composite DP signal.
A WDM system may also include an optical receiver (Rx). The optical receiver may be associated with a polarization beam splitter (PBS) that receives an optical signal (e.g., a WDM signal), splits the received optical signal, and provides two optical signals (e.g., associated with orthogonal polarizations) associated with the received optical signal. The optical receiver may also be associated with an optical demultiplexer circuit (referred to as a “demultiplexer”) configured to receive the optical signals provided by the PBS and demultiplex each one of the optical signals into individual optical signals. Additionally, the optical receiver may include receiver components to convert the individual optical signals into electrical signals, and output the data carried by those electrical signals.
The optical transmitter (Tx) and the optical receiver (Rx), in an optical communication system, may support communications over a number of wavelength channels. For example, a pair of optical transmitter/receiver may support ten channels, each spaced by, for example, 200 GHz. The set of channels supported by the optical transmitter and the optical receiver can be referred to as a channel grid. Channel grids for the optical transmitter and the optical receiver may be aligned to standardized frequencies, such as those published by the Telecommunication Standardization Sector (ITU-T). The set of channels supported by the optical transmitter and the optical receiver may be referred to as an ITU frequency grid.
In a WDM system, each wave (e.g., signal) of the optical transmitter may modulate the phase and/or amplitude of a laser in order to convey data (via the signal) to the optical receiver where the signal may be demodulated such that data, included in the signal, may be recovered. A particular modulation format (e.g., quadrature phase-shift keying (QPSK), quadrature amplitude modulation (QAM), binary phase-shift keying (BPSK), or the like) may be used to modulate the input signal. The signal may be subject to phase noise during transmission. The different modulation formats and/or the noise may result in a tradeoff between capacity and reach.
The optical receiver may include a digital signal processor (DSP) that tracks a phase of a modulated signal by applying a carrier phase recovery function. Phase tracking may permit the optical receiver to compensate for random phase fluctuations, associated with lasers of the optical transmitter and/or the optical receiver, so that the optical receiver may properly decode transmitted bits in the signal. However, phase tracking, when subjected to a large amount of noise, may momentarily lose lock and cause a cycle slip. A cycle slip may occur when the phase of the signal locks at a first phase (e.g., zero (0) degrees), and then transitions to and re-locks at a second phase (e.g., ninety (90) degrees). The QPSK constellation may include ninety degrees of symmetry that is invariant over ninety degree rotations and is a valid lock point. A transition time from zero to ninety degrees may generally be on an order of a time constant of a phase estimation process.
A ninety degree phase ambiguity can be resolved by differential encoding in the optical transmitter and differential decoding in the optical receiver. However, such an approach doubles an error rate at the optical receiver, which causes the overall optical system to tolerate less noise at the optical receiver. Another approach inserts two consecutive pilot symbols, for every sixty-four (64) information-carrying symbols, in a signal generated by the optical transmitter. The two pilot symbols may be used by the optical receiver for detecting ninety degree phase ambiguity and for rotating the information-carrying symbols based on a phase detected with the two pilot symbols. However, such an approach determines a location of cycle slips with an uncertainty of +/−thirty-three (33) symbols. This uncertainty results in a considerable number of decoded bits with an inverted sign. At high cycle slip rates, such as 10−4 (e.g., a cycle slip every 104 symbols), the rate of sign inversions may approach 10−3. Such a high rate of sign inversions can significantly degrade a performance of a forward error correction (FEC) decoder in the optical receiver.